MU DIVISION

Question 19

Differential Equations★★★Question Bank

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Question

Let

F(x)

and

G(x)

be continuous, differentiable functions such that there exists a continuous function

h(x)

with

F'(x)=h(x)G(x)

and

G'(x)=h(x)F(x)

. If

F(0)=1

F(1)=\frac{25}7

G(0)=0

, and

G(1)=\frac{24}7

, find

\int_0^1h(x)\,dx.

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